Abstract: In this paper we present the connection between scattering amplitudes in momentum space and wave functions in coordinate space, generalizing previous work done for s-waves to any partial wave. The relationship to the wave function of the residues of the scattering amplitudes at the pole of bound states or resonances is investigated in detail. A sum rule obtained for the couplings provides a generalization to coupled channels, any partial wave and bound or resonance states, of Weinberg's compositeness condition, which was only valid for weakly bound states in one channel and s-wave. An example, requiring only experimental data, is shown for the rho meson indicating that it is not a composite particle of pi pi and K (K) over bar but something else.

Abstract: We investigate the decay of f(1) (1285) > pi K (K) over bar with the assumption that the f(1) (1285) is dynamically generated from the K*(K) over bar – cc interaction. In addition to the tree level diagrams that proceed via f(1)(1285) -> K*(K) over bar – cc -> pi K (K) over bar, we take into account also the final state interactions of K (K) over bar -> K (K) over bar and pi K -> pi K. The partial decay width and mass distributions of f(1) (1285) -> pi K (K) over bar are evaluated. We get a value for the partial decay width which, within errors, is in fair agreement with the experimental result. The contribution from the tree level diagrams is dominant, but the final state interactions have effects in the mass distributions. The predicted mass distributions are significantly different from phase space and tied to the K*(K) over bar – cc nature of the f(1) (1285) state.

Abstract: We have studied the production and decay of the f(1) (1285) into pi a(0)(980) and K* (K) over bar as a function of the mass of the resonance and find a shoulder around 1400 MeV, tied to a triangle singularity, for the pi a(0)(980) mode, and a peak around 1420 MeV with about 60 MeV width for the K* (K) over bar mode. Both of these features agree with the experimental information on which the f(1)(1420) resonance is based. In addition, we find that if the f(1)(1420) is a genuine resonance, coupling mostly to K* (K) over bar as seen experimentally, one finds unavoidably about a 20% fraction for pi a(0)(980) decay of this resonance, in drastic contradiction with all experiments. Altogether, we conclude that the f(1)(1420) is not a genuine resonance, but the manifestation of the pi a(0)(980) and K* (K) over bar decay modes of the f(1)(1285) at higher energies than the nominal one.

Abstract: After discussing the OZI suppression of one light meson exchange in the interaction of with isospin I = 1 , we study the contribution of the two-pion exchange to the interaction and the exchange of heavy vectors, J/psi for diagonal transitions and D-* for transitions of to J/psi rho. We find these latter mechanisms to be weak, but enough to barely bind the system in J = 2 with a mass around 4000 MeV, while the effect of the two-pion exchange is a net attraction, though weaker than that from heavy-vector exchange. We discuss this state and try to relate it to the Z (c) (4025) state, above the threshold, claimed in an experiment at BES from an enhancement of the distribution close to threshold. Together with the results from a recent reanalysis of the BES experiment showing that it is compatible with a J = 2 state below threshold around 3990 MeV, we conclude that the BES experiment could show the existence of the state that we find in our approach.

Abstract: We make a theoretical study of the eta(1405) -> pi(0)f(0)(980) and eta(1405) -> pi(0)a(0)(980) reactions with an aim to determine the isospin violation and the mixing of the f(0)(980) and a(0)(980) resonances. We make use of the chiral unitary approach where these two resonances appear as composite states of two mesons, dynamically generated by the meson-meson interaction provided by chiral Lagrangians. We obtain a very narrow shape for the f(0)(980) production in agreement with a BES experiment. As to the amount of isospin violation, or f(0)(980) and a(0)(980) mixing, assuming constant vertices for the primary eta(1405) -> pi K-0 (K) over bar and eta(1405) -> pi(0)pi(0)eta production, we find results which are much smaller than found in the recent experimental BES paper, but consistent with results found in two other related BES experiments. We have tried to understand this anomaly by assuming an I = 1 mixture in the eta(1405) wave function, but this leads to a much bigger width of the f(0)(980) mass distribution than observed experimentally. The problem is solved by using the primary production driven by eta' -> K*(K) over bar followed by K* -> K pi, which induces an extra singularity in the loop functions needed to produce the f(0)(980) and a(0)(980) resonances. Improving upon earlier work along the same lines, and using the chiral unitary approach, we can now predict absolute values for the ratio Gamma(pi(0), pi(+)pi(-))/Gamma(pi(0), pi(0)eta) which are in fair agreement with experiment. We also show that the same results hold if we had the eta(1475) resonance or a mixture of these two states, as seems to be the case in the BES experiment.